Yes dogs will vomit up things that don't settle well in their stomachs. Be aware though that some of that plastic might stay in his stomach depending on how much he chewed and how big the pieces are.

You should consider taking your pup to the vet just in case, because an intestinal blockage can end up killing your dog in not caught in time. You also need to be concerned about sharp pieces piercing intestinal linings which is also a very serious occurance.

Call your vet and discuss what your pup ingested and based on what it was, how much of it he ate. Your vet may want to do x-rays to check that nothing is lodged or big enough that it will cause problems later.

Even when people are vigiliant in watching their dogs, they still get into things, it's a fact of life. Our Brody had emergency surgery over Labor Day weekend to remove a peach pit lodged in his intestines. We don't have any idea when and where it got it from and this guy gets a LOT of supervision lol!